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Explore the intersection between software and mathematics. Michael L Perry takes you on a journey through the history of computing, information theory, cryptography, distributed systems, and...
The number of degrees of freedom in a system is equal to its number of unknowns minus its number of equations. That is also equal to the num...
Leslie Lamport wrote a paper describing the Paxos algorithm in plain English. This is an algorithm that guarantees that a distributed system...
The Pythagoreans were a cult of Greek mathematicians that believed that all things were composed of large enough integers. Their leader, Pyt...
Euclid's Elements takes a disciplined, formal approach to proving assertions based only on simple axiomatic statements. While most of these...
The Lambda Calculus uses simple replacement to compute expressions. However, it does not define a way to replace a parameter of a function w...
Claude Shannon followed up one incredibly important paper with a second of even greater significance. In Communication Theory of Secrecy Sys...
in a translation of a paper on the Analytical Engine, Ada Lovelace improved upon L. F. Menambrea's work by applying rigor to the calculation...
The Difference Engine was a mechanical computer that could calculate tables of numbers based on polynomials. The amazing thing is, though, t...
Alonzo Church invented The Lambda Calculus as a simple set of rules that, when applied correctly, could compute anything that you could do w...
Listener Richard Allen writes to ask about proving enough of a program correct to constrain the number of tests that must be written. I resp...
In 2000, Eric Brewer presented the CAP Conjecture to the Symposium on Principles of Distributed Computing. This states that a distributed sy...
Knowing that a directed graph is acyclic is useful. If you construct directed graphs in a certain way, then you can prove that they have no...
In a directed acyclic graph, we can use reachability to determine a partial order. But sometimes we want a total ordering of the nodes to ac...
A fully ordered set is one in which we can tell for any two members which one comes before the other. Think integers. A partially ordered se...
The number of degrees of freedom in a solution should match the number in the problem. If you have extra degrees of freedom, then you have t...
In the .NET Socket API, if you call methods in the wrong order, the Socket class will throw an exception. Wouldn't it be better if it guided...
FirstOrDefault is an extension method used in Linq. It is often used incorrectly, leading to exceptions or ignored data. Learn techniques fo...
Code Contracts let you express predicates in C# code. This Visual Studio plug in and associated library checks your assertions. It can perfo...
Apply the principles of predicate calculus to creating reliable software. Use a technique inspired by algebra to confidently change the stru...